Problem: $A$ $B$ $C$ If: $ AB = 9x + 9$, $ BC = 8x + 9$, and $ AC = 154$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 9} + {8x + 9} = {154}$ Combine like terms: $ 17x + 18 = {154}$ Subtract $18$ from both sides: $ 17x = 136$ Divide both sides by $17$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $BC$ $ BC = 8({8}) + 9$ Simplify: $ {BC = 64 + 9}$ Simplify to find ${BC}$ : $ {BC = 73}$